Now, as for what Paul was teaching. We just saw how the Jerusalem elders were pleased with what Paul was doing among the gentiles, and gave judgement (referenced multiple times in multiple chapters) that they should not be troubled with keeping the law.
Was Paul teaching anything that could be construed as consistent with the idea that gentiles still needed to circumcise their children?
 
Let's see:
1 Corinthians 7
For neither circumcision counts for anything nor uncircumcision, but keeping the commandments of God.
Romans 3
Since God is one—who will justify the circumcised by faith and the uncircumcised through faith.
Romans 4
Is this blessing then only for the circumcised, or also for the uncircumcised? We say that faith was counted to Abraham as righteousness. How then was it counted to him? Was it before or after he had been circumcised? It was not after, but before he was circumcised. He received the sign of circumcision as a seal of the righteousness that he had by faith while he was still uncircumcised. The purpose was to make him the father of all who believe without being circumcised, so that righteousness would be counted to them as well,
Romans 2
For circumcision indeed is of value if you obey the law, but if you break the law, your circumcision becomes uncircumcision. So, if a man who is uncircumcised keeps the precepts of the law, will not his uncircumcision be regarded as circumcision? Then he who is physically uncircumcised but keeps the law will condemn you who have the written code and circumcision but break the law. For no one is a Jew who is merely one outwardly, nor is circumcision outward and physical. But a Jew is one inwardly, and circumcision is a matter of the heart, by the Spirit, not by the letter. His praise is not from man but from God.
 
Galatians 2
Then after fourteen years I went up again to Jerusalem with Barnabas, taking Titus along with me. 2 I went up because of a revelation and set before them (though privately before those who seemed influential) the gospel that I proclaim among the Gentiles, in order to make sure I was not running or had not run in vain. 3 But even Titus, who was with me, was not forced to be circumcised, though he was a Greek.
12 For before certain men came from James, he was eating with the Gentiles; but when they came he drew back and separated himself, fearing the circumcision party. 13 And the rest of the Jews acted hypocritically along with him, so that even Barnabas was led astray by their hypocrisy. 14 But when I saw that their conduct was not in step with the truth of the gospel, I said to Cephas before them all, "If you, though a Jew, live like a Gentile and not like a Jew, how can you force the Gentiles to live like Jews?"
 
1 Corinthians 7
Was anyone at the time of his call already circumcised? Let him not seek to remove the marks of circumcision. Was anyone at the time of his call uncircumcised? Let him not seek circumcision.
Galatians 5
For freedom Christ has set us free; stand firm therefore, and do not submit again to a yoke of slavery.
2 Look: I, Paul, say to you that if you accept circumcision, Christ will be of no advantage to you. 3 I testify again to every man who accepts circumcision that he is obligated to keep the whole law. 4 You are severed from Christ, you who would be justified by the law; you have fallen away from grace. 5 For through the Spirit, by faith, we ourselves eagerly wait for the hope of righteousness. 6 For in Christ Jesus neither circumcision nor uncircumcision counts for anything, but only faith working through love.
6 Galatians
12 It is those who want to make a good showing in the flesh who would force you to be circumcised, and only in order that they may not be persecuted for the cross of Christ. 13 For even those who are circumcised do not themselves keep the law, but they desire to have you circumcised that they may boast in your flesh.
 
 
(Jeremiah here for reference with the applicable Pauline quotes)
Jeremiah 4
Circumcise yourselves to the Lord; remove the foreskin of your hearts, O men of Judah and inhabitants of Jerusalem; lest my wrath go forth like fire, and burn with none to quench it, because of the evil of your deeds."
Jeremiah 9
"Behold, the days are coming, declares the Lord, when I will punish all those who are circumcised merely in the flesh— Egypt, Judah, Edom, the sons of Ammon, Moab, and all who dwell in the desert who cut the corners of their hair, for all these nations are uncircumcised, and all the house of Israel are uncircumcised in heart."
Colossians 2
In him also you were circumcised with a circumcision made without hands, by putting off the body of the flesh, by the circumcision of Christ,
Phillipians 3
2 Look out for the dogs, look out for the evildoers, look out for those who mutilate the flesh. 3 For we are the circumcision, who worship by the Spirit of God and glory in Christ Jesus and put no confidence in the flesh—
...
For his sake I have suffered the loss of all things and count them as rubbish, in order that I may gain Christ 9 and be found in him, not having a righteousness of my own that comes from the law, but that which comes through faith in Christ, the righteousness from God that depends on faith—
 
 
 
 
Paul tells us the following:
 
-He says that we have the circumcision of Christ, the circumcised heart.
-He says that the truly circumcised are those who worship by the Spirit of God and glory in Christ Jesus, without regards for fleshly circumcision.
-He makes it clear that physical circumcision means absolutely nothing with regards to salvation.
-He says that physical circumcision has nothing to do with being declared righteous.
-He says that Peter lived like a gentile, and that gentiles should not be expected to live like Jews.
-He assures us that it was not necessary for Titus to be circumcised in the presence of the elders at Jerusalem, in contrast with Timothy whom Paul circumcised for the sake of non-christian Jews.
-He equates physically circumcising yourself with keeping the law of Moses.
-He says that we are not obligated to keep the mosaic law.
-He equates circumcision with putting a yoke of slavery on, in contrast with the freedom of Christ
-He says that those who were circumcised did not keep the rest of the law anyway.
 
 
Paul did not say anything that is consistent with the idea that gentiles should continue circumcising their infants.
Nor is there anything from scripture or from the culture at the time of Christ that would suggest it was acceptable for someone under the mosaic covenant to remain uncircumcised.
 
And that's not even getting into the entirety of Paul's comments on law, which would make it clear he cannot be teaching the necessity of circumcision for gentile infants because he teaches that keeping the mosaic law is itself no longer necessary for those who are led by the Spirit (Galatians 5 as a clear example)
Because he set Israel apart to be a Holy People who obeyed his commandments and to separate them from the gentiles, for "All generations" with "perpetual" statutes
God does want a people Holy, set apart - People with circumcised hearts.
Christ said that the world would know His followers by their love for each other.
John 13
34 "A new command I give you: Love one another. As I have loved you, so you must love one another. 35 By this everyone will know that you are my disciples, if you love one another."
So, how are you known to the world around you? By your love for others, or by your fleshly observances?